Stability (R²) — Return

R² of the log-cumulative Return curve vs time. 1.0 = perfectly smooth equity curve, 0 = no trend.

Computed from: Equity curve
Scope: Single report
Range: 0 – 1
Direction: Higher is better

Basis

Computed on the close-to-close Return Series (money-weighted)

Stability (R²) measures how straight an equity curve is — how cleanly a single straight line fits the cumulative curve over time. It runs from 0 to 1: a value near 1 means the curve marches up (or down) in an almost perfect line, while a value near 0 means it wanders with no steady trend. In plain words, R² is the share of the curve's movement that a straight line explains — 1 is a ruler-straight line, 0 is pure noise.

The catch lives in that word straight: stability says nothing about which way the line points. A steadily losing account draws a straight line too, and scores just as high.

Key takeaways

What it is — the R² (coefficient of determination) of a straight-line fit to the cumulative equity curve against time. One number, 0 to 1, for how linear the growth is.
Read it as — how consistent the compounding is. High = a smooth, predictable climb; low = lumpy and erratic. It measures the shape of the curve, never its slope.
Why it matters — high R² ≠ profitable. A straight line down has R² ≈ 1. Stability tells you the edge is steady, not that there's an edge at all — always read it next to a return number like CAGR (the account's actual yearly growth rate): stability says how smooth, CAGR says which way and how much.
In EquityTruth — R² of a line fit to log cumulative equity vs the trading-day index on the Return and TWR curves, and to linear cumulative P&L on the Profit curve. Always close-to-close.

How it's calculated

Fit a straight line (ordinary least squares) through the cumulative equity curve plotted against time, then ask how much of the curve's variation that line accounts for. That fraction is R². A curve that hugs its trend line leaves little unexplained and scores near 1; a curve that zig-zags around the line leaves a lot unexplained and scores low.

Stability = R² of a straight-line fit to log-equity vs time

log-equity: the natural log of cumulative equity, indexed to the start (log(equityₜ / equity₀))
time: the trading-day index 0, 1, 2, … (equal spacing, one step per day)
R²: how much of the curve's up-and-down a single straight line accounts for: 1 = the line explains everything (ruler-straight), 0 = it explains nothing

In this product: EquityTruth computes the R² of an OLS line regressed on the daily close series. On the Return and TWR curves it fits log cumulative equity (steady compounding plots as a straight line in log space); on the Profit curve it fits the raw cumulative P&L linearly (no log). The result is naturally in [0, 1]; it returns 0 for fewer than three points or a flat curve.

On the Return curve, stability is fit to log equity, so steady percentage compounding — the same growth rate month after month — reads as a straight line and scores near 1. Deposits and withdrawals bend the curve, so a lumpy funding history can drag it down.

What it tells you

Value	Reading	Notes
< 0.5	Erratic	No steady trend — lumpy, regime-driven, or too few data points.
0.5 – 0.8	Moderately steady	A discernible trend with real wobble around it.
0.8 – 0.95	Steady	A clean, consistent climb — provided the slope is upward.
> 0.95	Suspiciously smooth	Almost a perfect line. On a real leveraged account that is unusual — confirm it’s rising, then ask how the smoothness was achieved. Manufactured straightness (grids, a cherry-picked window) lives here as often as genuine quality.

These describe smoothness only — a smoothly losing account still lands in the top band. High R² is smooth, not automatically good: read every band with the slope in mind. A 0.97 on a losing account is a reliably bleeding strategy, not a winning one.

Read stability and slope as a pair — only one quadrant is worth chasing:

Linear and rising — the goal: a steady, compounding edge.
Linear and falling — a reliable loser; the straight line is bleeding you out.
Jagged and rising — a winner you can't trust to repeat; the profit came in lucky lumps.
Jagged and falling — just noise going nowhere.

Same start, same finish — but the straight curve scores R² near 1 while the jagged one scores low. Stability measures the path's straightness, not where it ends.

Worked example

Picture two real accounts that both grow from 100 to 150. The first adds a near-steady ~4% each step, so its growth curve climbs in an almost perfect line — its fitted line leaves only a little leftover scatter, and R² lands near 0.99. (A perfectly constant rate would score exactly 1.0; real jitter pulls it just under.) The second lurches up and down, overshooting and giving back, before stumbling to the same 150. A straight line fits it poorly — much of its movement is left unexplained — so R² might be only 0.3. Identical return, opposite consistency. That gap is exactly what stability captures and what total return alone hides.

Pitfalls

Pitfalls & caveats

High R² is smooth, not profitable. A straight line down has R² ≈ 1. Stability is blind to direction — it never tells you the account is making money. Always pair it with CAGR or total return before reading high as good.
Says nothing about slope or magnitude. Two accounts can both score 0.98 while one earns 5% a year and the other 50%. R² rates the straightness of the line, not its steepness.
A too-straight line is a warning, not a trophy — especially on leverage. Genuine directional edges are lumpy; they have losing streaks, so they dent R². The strategies that draw a beautifully straight line are disproportionately the ones hiding risk in the tail — grids, martingales, averaging into losers — collecting small steady gains until the one trade that doesn't come back. R² sees only the path that already happened; it is structurally blind to the blow-up it's setting up. On a leveraged forex account, an R² above ~0.97 should make you more suspicious, not less. Cross-check with max drawdown and the trade distribution.
Curve-fittable and window-sensitive. R² rises as you shorten or cherry-pick the window — lop off the bad month and the line straightens. A high R² over three months means far less than the same number over three years. Always check the sample length and whether the window was chosen for you.
Sensitive to the fit. Log vs linear changes the answer: compounding is straight in log space but curved in dollars. EquityTruth uses log on Return/TWR and linear on Profit — compare like with like.
Close-to-close (measured from each day's closing value, not its swings between marks), so intraday excursions don't enter the fit.

Stability vs Volatility

Both sound like "smoothness," but they measure different things. Volatility is the dispersion of period returns — how far each day strays from the average day. Stability is the linearity of the cumulative curve — how well one line fits the whole path. A curve can carry moderate volatility and still score a high R² if its noise is symmetric around a clean trend: the daily wiggles cancel out and the line stays straight. Volatility asks "how big are the bumps?"; stability asks "do the bumps add up to a straight road?" The dangerous case is when the noise is not symmetric — many small gains and a rare huge loss (the grid/short-vol profile) — because that skew is exactly what a straight-line R² can't see and ordinary volatility under-reports.

Stability is a consistency lens; its companions sharpen it. Win Days % counts how often days finish green, Volatility sizes the day-to-day swings, the Sharpe ratio sets return against that dispersion, and CAGR supplies the slope that stability deliberately ignores. For the hidden-tail case a suspiciously high R² can mask, cross-check max drawdown and the Ulcer Index.